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If \(Z\) is an integer, what is the value of \(Z\) ? 1. \(Z^2 \le 0\) 2. \(Z^3 \le 0\) Source: GMAT Club Tests  hardest GMAT questions Does anyone has an explanation for A)



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16 Nov 2008, 10:33
GMAT scope includes only real numbers. Hence, from stmt1: Z will be real on if Z = 0. Hence, sufficient.



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16 Nov 2008, 16:45
rishi4you wrote: If Z is an integer, what is the value of z
1) Z^2<=0 (read as z raised to the power 2 is less than equal to 0) 2) z^3<=0 (read as z raised to the power 3 is less than equal to 0)
A)Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient B)Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient C)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient D)EACH statement ALONE is sufficient E)Statements (1) and (2) TOGETHER are NOT sufficient
Does anyone has an explanation for A) A. z = 0. 1: z cannot be ve. so it has to be 0. suff. 2: z can be ve or 0. so nsf..
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Re: m1#23 [#permalink]
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16 Nov 2008, 19:54
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I guess you already have your answer but I'll just type it out thoroughly.
(a) notes that square of a number is less than or equal to zero. You know that square of any positive or negative integer is positive, so the value cannot be less than 0. So only answer is "zero". Sufficient.
(b) notes that raised to 3 power is less than or equal to 0. 0x0x0 = true, 1x1x1 is less than 0 = true. You have multiple values, so this one is insufficient.
Hence the answer is A.



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Re: m01#23 [#permalink]
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21 Sep 2010, 06:11
it's A.
given that Z is an integer , so Z Sq cannot be negative. It has to be 0.Sufficient
When Z power 3 is ve , it could be any ve integer. not Sufficient.



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Re: m01#23 [#permalink]
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21 Sep 2010, 06:26
As per the equation one we have Z^2 <=0 that means either Z is 0 or not real. In case of GMAT we only need to consider real numbers . So A is sufficient.
As per B we have Z^3 <= 0 , so Z can be either 0 or negative , therefore we dont have unique answer .So B is not sufficient
Therefore A is the answer.



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Re: m01#23 [#permalink]
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21 Sep 2010, 06:37
For any integer Z, Z^2 is always positive, ie Z^2 >= 0 (1) states that Z^2 <= 0
Thus we can figure that Z^2 = 0, ie Z=0
Z^3 can have positive and negative values (2) states that Z^3 <= 0 For z=0, Z^3 = 0 For z=1, Z^3 = 1, both are <=0, therefore we cannot reach a conclusion.



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Re: m01#23 [#permalink]
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21 Sep 2010, 06:57
Is it me, or have the past few quant questions of the day (including this one) been far too easy?
I don't mean to sound high and mighty. I mean I know that I am at a 600700 level for quant, so these should be pretty challenging for me, but the last few have not been. Thoughts?



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Re: m01#23 [#permalink]
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21 Sep 2010, 07:28
Its A. 1. Squares are nonnegative. So Z is 0 2. Z can be 0 or negative number



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21 Sep 2010, 08:16
Z must be an integer rules out imaginary numbers.
Zsquared must be positive but cannot due to z <= 0 limit so Z must be zero. Suff
Zcubed allows for negative numbers. Insuff.



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Re: m01#23 [#permalink]
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21 Sep 2010, 19:15
A : if and only if Z=0 : OK B : any integer that satisfies Z<=0 : so NG
IMO  A



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22 Sep 2010, 12:21
After asking google whether zero was an integer, I brilliantly chose A.



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22 Sep 2010, 13:49
GaryDunn wrote: GMAT TIGER wrote: rishi4you wrote: If Z is an integer, what is the value of z
1) Z^2<=0 (read as z raised to the power 2 is less than equal to 0) 2) z^3<=0 (read as z raised to the power 3 is less than equal to 0)
A)Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient B)Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient C)BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient D)EACH statement ALONE is sufficient E)Statements (1) and (2) TOGETHER are NOT sufficient
Does anyone has an explanation for A) A. z = 0. 1: z cannot be ve. so it has to be 0. suff. 2: z can be ve or 0. so nsf.. Can someone explain the ve/ve notation please. I think it is shorthand (laziness?) for positi ve (+ve) and negati ve (ve).



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Re: m01#23 [#permalink]
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23 Sep 2010, 00:24
I don't think i have a better explanation than what have been given above. Generally, if x^2<0, then x must be an invalid number on the number line. x must be 0, A is sufficient.
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Re: m01#23 [#permalink]
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23 Sep 2011, 04:54
easy one. Statement 1 is sufficient to answer the question. keep in mind that GMAT never ask for Imaginary numbers. it works on Real No only.
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Re: m01#23 [#permalink]
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14 Nov 2011, 22:21
Statement 1 tells us that Z must be equal to zero.
Statement 2 tells us that Z can be either zero or any negative integer.
So statement 1 is sufficient, statement 2 is insufficient. Ans A.



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Re: m01#23 [#permalink]
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25 Sep 2012, 06:31
1) Z^2 will always be a NONNEGATIVE number. Therefore, if Z^2<=0, this means that z<=0. Because it cannot be negative, it must be 0. SUFFICIENT.
2) Z^3 can be a negative or positive or 0. if Z^3 <=0, it could be any number equal or less than 0. INSUFFICIENT.
Answer is A.



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29 Oct 2013, 05:50
Not sure if this question is correct; Bunuel / some one else can u please clarify me here.
According to first statement z=0 is being taken; but 0*0 will give undefined so how can we equate it to zero.
Pls help



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29 Oct 2013, 06:52










